Delivery processing apparatuses (postal sorters) that are used by postal services and the like perform processing in which a delivery sort destination corresponding to a region to which the address belongs is specified based on the address that is e.g. written on a delivery object, and the delivery object is transported to one out of a plurality of stackers (stackers) that corresponds to that delivery sort destination. At that time, when there are many delivery objects that are to be delivered to a specific region, it may happen that the stacker corresponding to that region becomes full, and to address this, a technique is known in which backup stackers are kept ready, and the delivery sort destination is temporarily assigned to such a backup stacker. However, in the conventional technology, there are cases in which the sorting and stacking of the delivery objects cannot be carried out efficiently.